The Wildcats (16-1) trailed by 12 midway through the second half and could not make a shot against one of the top defensive teams in the nation.
Led by Jordan Williams, the Terps (11-6) were 9 minutes from the signature win against a Top 25 team that they've been craving.
Fisher snatched it from them and sent the Wildcats streaking into Monday's Big East showdown at No. 10 Connecticut. Fisher hit a pair of 3s during the spurt and sent the crowd at their off-campus NBA home into a frenzy.
After opening the second half 4 of 14 from the field, the Wildcats went on a tear.
The Terps went about as cold as a team can get down the stretch - missing eight straight shots over 7:14 before Williams scored to made it 66-61.
The Terps closed within three when Maalik Wayns buried a 3-pointer to give the Wildcats some space.
Wayns and Fisher were dynamic in the backcourt and again showed why the Wildcats are never out of any game. Wayns led the Wildcats with 22 points and combined with Fisher to shoot 14 for 25 - a big bailout for a team that shot 29 percent from the floor in the second half.
The Wildcats played without forward Maurice Sutton (disciplinary reasons) and went the second half without Dominic Cheek (injured left knee).
The Wildcats couldn't afford to let this win slip away, not with the Huskies and No. 4 Syracuse the next two games on the schedule.
The Wildcats forced turnovers and grabbed all the clutch rebounds down the stretch. Isiah Armwood grabbed 13 rebounds and Mouphtaou Yarou had 12 to dominate inside and help make up for sloppy shooting. Coach Jay Wright has perhaps his most well-rounded team in 10 seasons - Antonio Pena is their first consistent double-double threat at forward in years.
He did it again with 14 points and 10 rebounds.
The Terps came out with something to prove and crisp offense (12 assists on 15 baskets) sent them into halftime with a 36-33 lead. Williams was a rebound shy from a double-double at the break and the Terps were clicking.
They built the lead to 12 points and showed no signs of blowing the win. Williams had 25 points and 14 rebounds, and Dino Gregory and Adrian Bowie each had 10.
No one can accuse the Terps of having a soft schedule. They have lost to No. 1 Duke, No. 5 Pittsburgh, No. 16 Illinois, No. 19 Temple and now the ranked Wildcats.